Data structure: \(O = (W, A, Z, Y)\)
Underlying data generating process, \(P_{U,X}\)
## W A Z Y
## Min. :-3.71792 Min. :0.000 Min. :0.0000 Min. :0.0000
## 1st Qu.:-0.65715 1st Qu.:0.606 1st Qu.:0.0000 1st Qu.:0.0000
## Median : 0.01527 Median :1.987 Median :0.0000 Median :0.0000
## Mean : 0.01455 Mean :2.098 Mean :0.4828 Mean :0.2507
## 3rd Qu.: 0.68169 3rd Qu.:3.347 3rd Qu.:1.0000 3rd Qu.:1.0000
## Max. : 4.34792 Max. :5.000 Max. :1.0000 Max. :1.0000
## Summary of A given W < -1:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.000 1.331 2.656 2.623 3.930 5.000
## Summary of A given -1 < W <= 0:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0000 0.9508 2.2621 2.3268 3.6176 5.0000
## Summary of A given 0 < W <= 1:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0000 0.3793 1.7606 1.9012 3.0529 5.0000
## Summary of A given 1 < W:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.000 0.000 1.285 1.536 2.569 5.000
## CV selected lambda (from one sample): 0.00179663135270864
## The average of CV selected lambdas (from 1000 sample): 0.00167069905743632
## z=1:
## z=0:
## Undersmoothed lambda: 0.000291732819942546
## which is 0.162377673918872 * lambda_CV
## The average of unsersmoothed lambda (from 1000 sample): 0.000270475505996292
## which is 0.155768441258726 * the average of 1000 lambda_CV
## z=1:
## z=0:
## z=1:
## z=0:
## CV selected lambda (from one sample): 0.000284242765357572
## The average of CV selected lambdas (from 1000 sample): 0.00072537755501008
## z=1:
## z=0:
## Undersmoothed lambda: 4.61546790670303e-05
## which is 0.162377673918872 * lambda_CV
## The average of unsersmoothed lambda (from 1000 sample): 0.000103940431379792
## which is 0.146789904758241 * the average of 1000 lambda_CV
## z=1:
## z=0:
## z=1:
## z=0: